Fig. 1. Off-axis pumping and astigmatic conversion. (a) High-order HG modes motivated by off-axis pumping^[26]; (b) a pair of cylindrical lenses as the astigmatic mode converter^[29]; (c) one cylindrical lens as the astigmatic mode converter^[30]

Fig. 2. Lissajous and trochoidal patterns. (a) Lissajous light field and its transmission^[35];(b) trochoidal light field and its transmission^[36]

Fig. 3. Geometric modes light field. (a) Phase control of geometric modes^[41]; (b) verification of singularities in geometric modes light field^[42]

Fig. 4. Light field patterns of the transverse mode locking and the non-mode-locking vortex lattices^[45]. (a) The experimental result; (b) the simulation result

Fig. 5. Controllable Poincare beams^[53]. (a)(b)(c) Schematics of experimental set-up; (d)(e)(f)(g)(h) experimental results

Fig. 6. Design of SLM digital laser and its experimental results. (a) Holographic digital laser^[55];(b) loss-control digital laser^[56]

Fig. 7. The set-up and experimental results of the pump-shaping laser. (a) HG modes pump-shaping laser^[60];(b) vector vortex pump-shaping laser^[61]

Fig. 8. The method on the SLM modulation out of cavity. (a) Set-up and experimental results of dual phase modulation^[77]; (b) double-Fourier transform optical setup for the generation of scalar complex fields employing a CGH^[78]

Fig. 9. Light field patterns customization on CGH. (a) A variety of custom structured light field^[79];(b) 200 modes multiplex from a single SLM^[80]

Fig. 10. Extracavity pattern superposition produces the vortex array. (a) An experimental device for obtaining a vortex array by a Mach-Zehnder interferometer^[85]; (b) experimental results of multi-singularity vortex beam control by SLM based on the mode superposition method^[83]

Fig. 11. High order petaling Poincare vector beams obtained by superposition of out-of-cavity modes^[88].(a) Experimental set-up; (b) schematic

Fig. 12. Simultaneous generation of vector structured beams by out-of-cavity modes superposition and multi-channel multiplex technology^[89]. (a) Experimental set-up; (b) schematic; (c) experimental results

Fig. 13. Vortex beams produced by the metasurfaces. (a) The hexagonal-unit metasurface^[95]; (b) conversion of circularly polarized light to two arbitrary OAM beams^[100]